The discontinuous Galerkin method for fractal conservation laws

We propose, analyze, and demonstrate a discontinuous Galerkin method for fractal conservation laws. Various stability estimates are established along with error estimates for regular solutions of linear equations. Moreover, in the nonlinear case and whenever piecewise constant elements are utilized,...

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Bibliographic Details
Published inarXiv.org
Main Authors Cifani, Simone, Jakobsen, Espen R, Karlsen, Kenneth H
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.06.2010
Subjects
Conservation laws
Entropy of solution
Fractal analysis
Fractals
Galerkin method
Linear equations
Mathematics - Analysis of PDEs
Mathematics - Numerical Analysis
Nonlinear equations
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Summary:We propose, analyze, and demonstrate a discontinuous Galerkin method for fractal conservation laws. Various stability estimates are established along with error estimates for regular solutions of linear equations. Moreover, in the nonlinear case and whenever piecewise constant elements are utilized, we prove a rate of convergence toward the unique entropy solution. We present numerical results for different types of solutions of linear and nonlinear fractal conservation laws.
ISSN:2331-8422
DOI:10.48550/arxiv.0906.1092